Do not use a calculator in answering this question. It is given that complex numbers ${{z}_{1}}$ and

Question

Do not use a calculator in answering this question. It is given that complex numbers ${{z}_{1}}$ and ${{z}_{2}}$ are the roots of the equation ${{z}^{2}}-6z+36=0$ such that $\arg ({{z}_{1}})>\arg ({{z}_{2}})$. Find exact expressions of ${{z}_{1}}$ and ${{z}_{2}}$ in the form $r{{\mathrm{e}}^{\mathrm{i}	heta }}$, where $r>0$ and $-\pi [4] Find the complex number $\frac{{{z}_{1}}^{4}}{\mathrm{i}{{z}_{2}}}$ in exact polar form. [3] Find the smallest positive integer $n$ such that ${{z}_{2}}^{n}$ is a positive real number. [2]

Accepted Answer

(i) $z_1 = 6e^{i\frac{\pi}{3}}$, $z_2 = 6e^{-i\frac{\pi}{3}}$ (ii) $216\left[\cos\frac{5\pi}{6} - i\sin\frac{5\pi}{6}\right]$, $n = 6$

2016 CJC P1 Q8

2016 CJC P1 Q8

Video Solution:

Solution:

Solution locked